Problem: Solve for $x$, $ -\dfrac{6}{3x - 5} = \dfrac{x + 10}{6x - 10} + \dfrac{1}{3x - 5} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3x - 5$ $6x - 10$ and $3x - 5$ The common denominator is $6x - 10$ To get $6x - 10$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ -\dfrac{6}{3x - 5} \times \dfrac{2}{2} = -\dfrac{12}{6x - 10} $ The denominator of the second term is already $6x - 10$ , so we don't need to change it. To get $6x - 10$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ \dfrac{1}{3x - 5} \times \dfrac{2}{2} = \dfrac{2}{6x - 10} $ This give us: $ -\dfrac{12}{6x - 10} = \dfrac{x + 10}{6x - 10} + \dfrac{2}{6x - 10} $ If we multiply both sides of the equation by $6x - 10$ , we get: $ -12 = x + 10 + 2$ $ -12 = x + 12$ $ -24 = x $ $ x = -24$